One class of experiments for artificial selection uses targeted mutations that are inferred to be beneficial, using machine learning techniques to characterize genotype-phenotype maps [1]}. Another class of experiments relies on implementing feedback control to tune artificial selection during continuous evolution of molecules and proteins, to direct them towards a desired target [2]}, [3]}, [4]}, [5]}, [6]}. For example, implementing proportional-integral-derivative (PID) control [7]}, which is known for its role in cruise control during driving, has shown significant improvements for molecular optimization by directed continuous evolution [6]}. PID control is simple to implement in practice and it is relatively robust to errors, as its proportional term corrects for spontaneous error, the integrator reduces the impact of long run error, and derivative term would suppress overshooting by anticipating the impact of control [9]}. Still, PID is far from optimal and requires fine-tuning of control parameters for the system, which is often tedious and subject to uncertainty. Therefore, implementing a more principled optimal control approaches for molecular evolution, such the path integral control introduced here, can further optimize the continuous directed evolution experiments.
